Kinetic-ballooning-mode turbulence in low-average-magnetic-shear equilibria

McKinney, I. J.; Pueschel, M. J.; Faber, B. J.; Hegna, C. C.; Ishizawa, A.; Terry, P. W.

doi:10.1017/s0022377821000581

Title: Kinetic-ballooning-mode turbulence in low-average-magnetic-shear equilibria

Journal Article · Tue Jun 15 00:00:00 EDT 2021 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s0022377821000581· OSTI ID:1788257

^[1]; Pueschel, M. J. ^[2];

^[1]; Hegna, C. C. ^[1]; Ishizawa, A. ^[3]; Terry, P. W. ^[1]

Univ. of Wisconsin, Madison, WI (United States)
Eindhoven Univ. of Technology (Netherlands); Dutch Institute For Fundamental Energy Research, Eindhoven (Netherlands); Univ. of Texas, Austin, TX (United States)
Kyoto Univ. (Japan)

In this work, kinetic-ballooning-mode (KBM) turbulence is studied via gyrokinetic flux-tube simulations in three magnetic equilibria that exhibit small average magnetic shear: the Helically Symmetric eXperiment (HSX), the helical-axis Heliotron-J and a circular tokamak geometry. For HSX, the onset of KBM being the dominant instability at low wavenumber occurs at a critical value of normalized plasma pressure $$\beta ^{\rm KBM}_{\rm crit}$$ that is an order of magnitude smaller than the magnetohydrodynamic (MHD) ballooning limit $$\beta ^{\rm MHD}_{\rm crit}$$ when a strong ion temperature gradient (ITG) is present. However, $$\beta ^{\rm KBM}_{\rm crit}$$ increases and approaches the MHD ballooning limit as the ITG tends to zero. For these configurations, $$\beta ^{\rm KBM}_{\rm crit}$$ also increases as the magnitude of the average magnetic shear increases, regardless of the sign of the normalized magnetic shear. Simulations of Heliotron-J and a circular axisymmetric geometry display behaviour similar to HSX with respect to $$\beta ^{\rm KBM}_{\rm crit}$$ . Despite large KBM growth rates at long wavelengths in HSX, saturation of KBM turbulence with $$\beta > \beta _{\rm crit}^{\rm KBM}$$ is achievable in HSX and results in lower heat transport relative to the electrostatic limit by a factor of roughly five. Nonlinear simulations also show that KBM transport dominates the dynamics when KBMs are destabilized linearly, even if KBM growth rates are subdominant to ITG growth rates.

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Research Organization:: Univ. of Wisconsin, Madison, WI (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: FG02-93ER54222; FG02-04ER54742; FG02-89ER53291; FG02-99ER54546; AC02-05CH11231

OSTI ID:: 1788257

Journal Information:: Journal of Plasma Physics, Vol. 87, Issue 3; ISSN 0022-3778

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

References (60)

Finite beta stabilization of the kinetic ion mixing mode Pu, Yi-Kang; Migliuolo, Stefano Physics of Fluids, Vol. 28, Issue 6 https://doi.org/10.1063/1.864965	journal	January 1985
Finite beta trapped electron fluid mode Strauss, H. R. Physics of Fluids, Vol. 22, Issue 6 https://doi.org/10.1063/1.862700	journal	January 1979
A comparison of turbulent transport in a quasi-helical and a quasi-axisymmetric stellarator McKinney, I. J.; Pueschel, M. J.; Faber, B. J. Journal of Plasma Physics, Vol. 85, Issue 5 https://doi.org/10.1017/S0022377819000588	journal	September 2019
The second region of stability against ballooning modes Greene, J. M.; Chance, M. S. Nuclear Fusion, Vol. 21, Issue 4 https://doi.org/10.1088/0029-5515/21/4/002	journal	April 1981
Eliminating turbulent self-interaction through the parallel boundary condition in local gyrokinetic simulations Ball, Justin; Brunner, Stephan; C. J., Ajay Journal of Plasma Physics, Vol. 86, Issue 2 https://doi.org/10.1017/S0022377820000197	journal	March 2020
Stellarator Research Opportunities: A Report of the National Stellarator Coordinating Committee Gates, David A.; Anderson, David; Anderson, S. Journal of Fusion Energy, Vol. 37, Issue 1 https://doi.org/10.1007/s10894-018-0152-7	journal	February 2018
Transport properties of finite-β microturbulence Pueschel, M. J.; Jenko, F. Physics of Plasmas, Vol. 17, Issue 6 https://doi.org/10.1063/1.3435280	journal	June 2010
Stellarator microinstabilities and turbulence at low magnetic shear Faber, B. J.; Pueschel, M. J.; Terry, P. W. Journal of Plasma Physics, Vol. 84, Issue 5 https://doi.org/10.1017/S0022377818001022	journal	October 2018
Existence of ion temperature gradient driven shear Alfvén instabilities in tokamaks Zonca, Fulvio; Chen, Liu; Dong, J. Q. Physics of Plasmas, Vol. 6, Issue 5 https://doi.org/10.1063/1.873449	journal	May 1999
“Universal” instabilities from plasma moment equations Coppi, B. Physics Letters, Vol. 14, Issue 3 https://doi.org/10.1016/0031-9163(65)90569-X	journal	February 1965
Performance of Wendelstein 7-X stellarator plasmas during the first divertor operation phase Wolf, R. C.; Alonso, A.; Äkäslompolo, S. Physics of Plasmas, Vol. 26, Issue 8 https://doi.org/10.1063/1.5098761	journal	August 2019
Compressibility effects on ideal and kinetic ballooning modes and elimination of finite Larmor radius stabilization Kotschenreuther, M. Physics of Fluids, Vol. 29, Issue 9 https://doi.org/10.1063/1.865490	journal	September 1986
Kinetic ballooning modes in tokamaks and stellarators Aleynikova, K.; Zocco, A.; Xanthopoulos, P. Journal of Plasma Physics, Vol. 84, Issue 6 https://doi.org/10.1017/S0022377818001186	journal	December 2018
Transport and isomorphic equilibria Boozer, Allen H. Physics of Fluids, Vol. 26, Issue 2 https://doi.org/10.1063/1.864166	journal	January 1983
Shear, Periodicity, and Plasma Ballooning Modes Connor, J. W.; Hastie, R. J.; Taylor, J. B. Physical Review Letters, Vol. 40, Issue 6 https://doi.org/10.1103/PhysRevLett.40.396	journal	February 1978
Physical mechanism of enhanced stability from negative shear in tokamaks: Implications for edge transport and the L‐H transition Antonsen, T. M.; Drake, J. F.; Guzdar, P. N. Physics of Plasmas, Vol. 3, Issue 6 https://doi.org/10.1063/1.871928	journal	June 1996
Numerical techniques for parallel dynamics in electromagnetic gyrokinetic Vlasov simulations Maeyama, S.; Ishizawa, A.; Watanabe, T. -H. Computer Physics Communications, Vol. 184, Issue 11 https://doi.org/10.1016/j.cpc.2013.06.014	journal	November 2013
Experimental Demonstration of Improved Neoclassical Transport with Quasihelical Symmetry Canik, J. M.; Anderson, D. T.; Anderson, F. S. B. Physical Review Letters, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevLett.98.085002	journal	February 2007
Quantitative study of kinetic ballooning mode theory in simple geometry Aleynikova, Ksenia; Zocco, Alessandro Physics of Plasmas, Vol. 24, Issue 9 https://doi.org/10.1063/1.5000052	journal	September 2017
Some considerations on closed configurations of magnetohydrostatic equilibrium Palumbo, D. Il Nuovo Cimento B Series 10, Vol. 53, Issue 2 https://doi.org/10.1007/BF02710251	journal	February 1968
Multi-machine analysis of turbulent transport in helical systems via gyrokinetic simulation Ishizawa, A.; Kishimoto, Y.; Watanabe, T. -H. Nuclear Fusion, Vol. 57, Issue 6 https://doi.org/10.1088/1741-4326/aa6603	journal	April 2017
Controlling Turbulence in Present and Future Stellarators Xanthopoulos, P.; Mynick, H. E.; Helander, P. Physical Review Letters, Vol. 113, Issue 15 https://doi.org/10.1103/PhysRevLett.113.155001	journal	October 2014
Are Drift-Wave Eigenmodes Unstable? Ross, David W.; Mahajan, Swadesh M. Physical Review Letters, Vol. 40, Issue 5 https://doi.org/10.1103/PhysRevLett.40.324	journal	January 1978
On the role of numerical dissipation in gyrokinetic Vlasov simulations of plasma microturbulence Pueschel, M. J.; Dannert, T.; Jenko, F. Computer Physics Communications, Vol. 181, Issue 8 https://doi.org/10.1016/j.cpc.2010.04.010	journal	August 2010
Necessary and sufficient conditions for quasisymmetry Rodríguez, E.; Helander, P.; Bhattacharjee, A. Physics of Plasmas, Vol. 27, Issue 6 https://doi.org/10.1063/5.0008551	journal	June 2020
Alfvénic ion temperature gradient activities in a weak magnetic shear plasma Chen, W.; Ma, R. R.; Li, Y. Y. EPL (Europhysics Letters), Vol. 116, Issue 4 https://doi.org/10.1209/0295-5075/116/45003	journal	November 2016
A new class of quasi-omnigenous configurations Isaev, M. Yu; Nührenberg, J.; Mikhailov, M. I. Nuclear Fusion, Vol. 43, Issue 10 https://doi.org/10.1088/0029-5515/43/10/007	journal	September 2003
Instabilities due to Temperature Gradients in Complex Magnetic Field Configurations Coppi, B. Physics of Fluids, Vol. 10, Issue 3 https://doi.org/10.1063/1.1762151	journal	January 1967
Nonlinear Electromagnetic Stabilization of Plasma Microturbulence Whelan, G. G.; Pueschel, M. J.; Terry, P. W. Physical Review Letters, Vol. 120, Issue 17 https://doi.org/10.1103/PhysRevLett.120.175002	journal	April 2018
Microinstability theory in tokamaks Tang, W. M. Nuclear Fusion, Vol. 18, Issue 8 https://doi.org/10.1088/0029-5515/18/8/006	journal	August 1978
Ion temperature gradient‐driven ballooning mode in tokamaks Hirose, A.; Zhang, L.; Elia, M. Physics of Plasmas, Vol. 2, Issue 3 https://doi.org/10.1063/1.871437	journal	March 1995
On microinstabilities and turbulence in steep-gradient regions of fusion devices Pueschel, M. J.; Hatch, D. R.; Ernst, D. R. Plasma Physics and Controlled Fusion, Vol. 61, Issue 3 https://doi.org/10.1088/1361-6587/aaf8c1	journal	February 2019
Kinetic theory of collisionless ballooning modes Cheng, C. Z. Physics of Fluids, Vol. 25, Issue 6 https://doi.org/10.1063/1.863858	journal	January 1982
Electromagnetic effect on the toroidal ion temperature gradient mode Kim, J. Y.; Horton, W.; Dong, J. Q. Physics of Fluids B: Plasma Physics, Vol. 5, Issue 11 https://doi.org/10.1063/1.860623	journal	November 1993
Major results from the stellarator Wendelstein 7-AS Hirsch, M.; Baldzuhn, J.; Beidler, C. Plasma Physics and Controlled Fusion, Vol. 50, Issue 5 https://doi.org/10.1088/0741-3335/50/5/053001	journal	March 2008
Improved -particle confinement in stellarators with poloidally closed contours of the magnetic field strength Mikhailov, M. I.; Shafranov, V. D.; Subbotin, A. A. Nuclear Fusion, Vol. 42, Issue 11 https://doi.org/10.1088/0029-5515/42/11/102	journal	October 2002
Massively parallel Vlasov simulation of electromagnetic drift-wave turbulence Jenko, Frank Computer Physics Communications, Vol. 125, Issue 1-3 https://doi.org/10.1016/S0010-4655(99)00489-0	journal	March 2000
Goals and status of Heliotron J Obiki, T.; Sano, F.; Wakatani, M. Plasma Physics and Controlled Fusion, Vol. 42, Issue 11 https://doi.org/10.1088/0741-3335/42/11/302	journal	November 2000
Gyrokinetic simulations of magnetic reconnection Pueschel, M. J.; Jenko, F.; Told, D. Physics of Plasmas, Vol. 18, Issue 11 https://doi.org/10.1063/1.3656965	journal	November 2011
Quasi-helically symmetric toroidal stellarators Nührenberg, J.; Zille, R. Physics Letters A, Vol. 129, Issue 2 https://doi.org/10.1016/0375-9601(88)90080-1	journal	May 1988
Effects of parallel ion motion on electromagnetic toroidal ion temperature gradient modes in a fluid model Jarmén, A.; Anderson, J.; Malinov, P. Physics of Plasmas, Vol. 22, Issue 8 https://doi.org/10.1063/1.4928374	journal	August 2015
Kinetic electromagnetic instabilities in an ITB plasma with weak magnetic shear Chen, W.; Yu, D. L.; Ma, R. R. Nuclear Fusion, Vol. 58, Issue 5 https://doi.org/10.1088/1741-4326/aaaece	journal	March 2018
Gyrokinetic turbulence simulations at high plasma beta Pueschel, M. J.; Kammerer, M.; Jenko, F. Physics of Plasmas, Vol. 15, Issue 10 https://doi.org/10.1063/1.3005380	journal	October 2008
Quasi-Symmetry in Stellarator Research. 5. Status of Physics Design of Quasi-Axisymmetric Stellarators. 5.1. Physics Design of the National Compact Stellarator Experiment. Neilson, George H.; Zarnstorff, Michael C.; Lyon, James F. Journal of Plasma and Fusion Research, Vol. 78, Issue 3 https://doi.org/10.1585/jspf.78.214	journal	January 2002
Three-dimensional free boundary calculations using a spectral Green's function method Hirshman, S. P.; van RIJ, W. I.; Merkel, P. Computer Physics Communications, Vol. 43, Issue 1 https://doi.org/10.1016/0010-4655(86)90058-5	journal	December 1986
Foundations of nonlinear gyrokinetic theory Brizard, A. J.; Hahm, T. S. Reviews of Modern Physics, Vol. 79, Issue 2 https://doi.org/10.1103/RevModPhys.79.421	journal	April 2007
Gyrokinetic studies of trapped electron mode turbulence in the Helically Symmetric eXperiment stellarator Faber, B. J.; Pueschel, M. J.; Proll, J. H. E. Physics of Plasmas, Vol. 22, Issue 7 https://doi.org/10.1063/1.4926510	journal	July 2015
Three-dimensional equilibrium of the anisotropic, finite-pressure guiding-center plasma: Theory of the magnetic plasma Hall, Laurence S.; McNamara, Brendan Physics of Fluids, Vol. 18, Issue 5 https://doi.org/10.1063/1.861189	journal	January 1975
Kinetic Ballooning Mode with Negative Shear Hirose, A.; Elia, M. Physical Review Letters, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevLett.76.628	journal	January 1996
Toroidal drift modes driven by ion pressure gradients Horton, Wendell Physics of Fluids, Vol. 24, Issue 6 https://doi.org/10.1063/1.863486	journal	January 1981
Saturation and nonlinear electromagnetic stabilization of ITG turbulence Whelan, G. G.; Pueschel, M. J.; Terry, P. W. Physics of Plasmas, Vol. 26, Issue 8 https://doi.org/10.1063/1.5096252	journal	August 2019
Universal Eigenmode in a Strongly Sheared Magnetic Field Pearlstein, L. D.; Berk, H. L. Physical Review Letters, Vol. 23, Issue 5 https://doi.org/10.1103/PhysRevLett.23.220	journal	August 1969
Finite beta effects on ion temperature gradient driven modes Dong, J. Q.; Guzdar, P. N.; Lee, Y. C. Physics of Fluids, Vol. 30, Issue 9 https://doi.org/10.1063/1.866034	journal	September 1987
Kinetic equations for low frequency instabilities in inhomogeneous plasmas Antonsen, Thomas M.; Lane, Barton Physics of Fluids, Vol. 23, Issue 6 https://doi.org/10.1063/1.863121	journal	January 1980
Transport optimization in stellarators Mynick, H. E. Physics of Plasmas, Vol. 13, Issue 5 https://doi.org/10.1063/1.2177643	journal	May 2006
Gyrokinetic analysis of linear microinstabilities for the stellarator Wendelstein 7-X Xanthopoulos, P.; Jenko, F. Physics of Plasmas, Vol. 14, Issue 4 https://doi.org/10.1063/1.2714328	journal	April 2007
Gyrokinetic turbulence simulations of high-beta tokamak and helical plasmas with full-kinetic and hybrid models Ishizawa, A.; Maeyama, S.; Watanabe, T. -H. Nuclear Fusion, Vol. 53, Issue 5 https://doi.org/10.1088/0029-5515/53/5/053007	journal	April 2013
A geometry interface for gyrokinetic microturbulence investigations in toroidal configurations Xanthopoulos, P.; Cooper, W. A.; Jenko, F. Physics of Plasmas, Vol. 16, Issue 8 https://doi.org/10.1063/1.3187907	journal	August 2009
Trapped particles in toroidal magnetic systems Kadomtsev, B. B.; Pogutse, O. P. Nuclear Fusion, Vol. 11, Issue 1 https://doi.org/10.1088/0029-5515/11/1/010	journal	January 1971
Theory of ITG turbulent saturation in stellarators: Identifying mechanisms to reduce turbulent transport Hegna, C. C.; Terry, P. W.; Faber, B. J. Physics of Plasmas, Vol. 25, Issue 2 https://doi.org/10.1063/1.5018198	journal	February 2018

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